56.1.73 problem 73

Internal problem ID [8785]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 73
Date solved : Monday, January 27, 2025 at 04:58:36 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 x \left (t \right )+5 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 32

dsolve([diff(x(t),t) = x(t)-2*y(t), diff(y(t),t) = 2*x(t)+5*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

DSolve[{D[x[t],t]== x[t]-2*y[t],D[y[t],t] == 2*x[t]+5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -e^{3 t} (c_1 (2 t-1)+2 c_2 t) \\ y(t)\to e^{3 t} (2 (c_1+c_2) t+c_2) \\ \end{align*}